I finally decided to peek in this thread, and no offense intended, but boy is it a mess!
Although ultimately how recoil "harshness" is perceived is most likely an individual thing, I think that several posters here are on the right train of thought but we still don't have a good understanding of the issue. First of all, it is important not to over-think the issue. The most obvious factors are the average and maximum amounts of
force transferred to the pistol over a period of time, right? Right, so plugging the numbers given in the original post for the heaviest, slowest and fastest, lightest loads, we get the following results (I could show my work but that would bore most people, and I won't even bother rounding to the significant digits):
Magtech 158 LSWC (heavy and slow--just the way I like it, oh yeah)
m = 0.01023822778 kg
v = 230.124 m/s
x = 0.1016 m
a = 260615.43 m/s²
avg F = 2668.2401353226454 N
max F = 7569.4040578441668163209925194463 N
t = 0.88300220750551876379690949227373 ms
momentum = 2.35606192964472 kg*m/s
E = 271.09319774878077264 J
Federal Hydra-Shok 110 JHP (light and fast--the quickie round)
m = 0.0071278801 kg
v = 298.704 m/s
x = 0.1016 m
a = 439094.88 m/s²
avg F = 3129.815657163888 N
max F = 7569.4040578441668163209925194463 N
t = 0.68027210884353741496598639455782 ms
momentum = 2.1291262973904 kg*m/s
E = 317.9892707678510208 J
Legend: m = mass, v = velocity, x = barrel length (really delta x, the displacement), a = average acceleration, F = force, t = time in milliseconds, momentum happens to be equivalent to impulse in this case, and E = energy.
Converting back to pounds of force because that's how we roll here, the average recoil force exerted by the 158 grain bullet over the 0.883 ms it spends in the barrel is about 600 lb, while the 110 grain bullet exerts an average force of about 704 lb over 0.68 ms. As is typical for most calibers, the load with the heavier, slower bullet imparts a greater reactive impulse (greater total momentum transfer) while the load with the lighter, faster bullet puts greater force on the shooter, albeit for a shorter period of time. Some may feel that the greater force of the latter "hurts" more, while others perceive the recoil of the former as being heavier and perhaps harsher to them as a result. Try a few different rounds and decide for yourselves.
Well, there it is, the faster the bullet the more hurt you're gonna feel.
Not exactly in theory because bullet weight still matters, but that's how it pretty much works out anyway with most factory loads, so it's a decent rule of thumb for those in the "instantaneous force hurts more than total momentum" group.
"Well, there it is, the faster the bullet the more hurt you're gonna feel."
Per given weight, yes.
And in practice with most factory loads, too, even though the bullets are lighter, which results in less momentum. This kind of makes me wonder precisely how recoil should be defined--is it the average instantaneous force or the total momentum? Technically, I believe that it's the latter, but how we individually perceive recoil may beg to differ.
It's simple physics:
F = MV or
Force = Mass x Velocity
This works for both ends of the gun.
The formulas are actually F = ma and I = mv (simplified for this case).
There's a thread about this same recoil issue on another forum I'm on. That one is getting a little heated between a couple of folks. In thinking about it and this one I'm not really seeing anything about the acceleration rate of the bullet. The other thread combatants are talking about impulse.
Impulse (same as momentum for our purposes) is definitely a crucial factor, and I've included acceleration and the resultant amounts of force above to help complete the picture.
And that makes perfect sense if you look at it for overall impulse vs bullet energy.
Note that for a given caliber, a factory load can have greater energy but lower impulse than another factory load at the same time.
But in thinking about their equations and disscussions they didn't look at the time it takes for the bullets to reach their final speeds. And THAT is going to have a very big impact (excuse the pun
) on the recoil felt by your hand.
Yes, and I suspect that force is more significant for many people.
A light bullet that gets up to speed and leaves the gun super fast will feel a lot sharper than a heavy bullet taking a longer time to pick up speed and exit downrange. And I suspect this has a lot to do with how we perceive the impact pulse in our hand.
And of course this goes totally against waht rmfnla just posted. But while that equation is 100% right it doesn't look at the time taken to ramp up to that speed.
That's because there are two often opposing ways to gauge the perceived harshness of recoil--both of which are valid and feel different--as I hopefully managed to describe above.
Rmfnla, you've made a basic mistake in your statement as well. I think you meant to say;
A 125 grain at 1250 fps will NOT recoil worse than a 158 grain at the same muzzle energy.
Ah-ha! You just mentioned energy. Note that from the numbers I gave above, the relative energy of the two loads varies proportionally with their relative amounts of force. This is true from the underlying equations because the amount of displacement--in this case the barrel length--is the same 4" that is typically used to derive the published specifications of .38 Special cartridges. Energy is merely the amount of work, which is defined as applying a force over a distance, that is done on both the bullet and ultimately your hand. The greater the amount of energy involved, the harder your hand gets worked over, so to speak.
That's why for some people the greater energy that comes from greater force hurts more than the impulse/total momentum/recoil/whatever you want to call it. Those guys in the other forum know what they're talking about regarding recoil by the numbers but they're not seeing the whole picture.
And in addition to everything I've said, higher-pressure rounds tend to feel harsher to many people as well because they have a higher maximum or peak force. Most of us are already familiar with this phenomenon and refer to it in terms of "snappiness."
